We considered necessary and sufficient conditions for the Verma modules M(μ(u)) of twisted Yangian Y(o₂)  to be reducible. If the weight of M(μ(u)) was determined by a certain rational function,  we could obtain a proper submodule of M(μ(u)) through construction method, thus proving  that M(μ(u)) was reducible. If M(μ(u)) was reducible, we could obtain a rational function associated with u，thus  we gave a necessary condition for M(μ(u)) to be reducible was that the rational function was a Laurent expansion at u=∞.

Using the theories and methods of Lie algebra and linear algebra, the author studied local automorphism problem of Schrodinger algebra. Combining the results of local automorphisms of special linear Lie algebra and the forms of automorphisms of Schrodinger algebra, the author characterized local automorphisms of Schrodinger algebra.

Let R be an associative ring with an identity, and (L,A) be a complete duality pair. Firstly, we introduce the class GP⁽²⁾_L of Gorenstein homological modules with respect to the complete duality pair (L,A). Secondly,  we study some properties of GP⁽²⁾_L. Finally, we prove that GP⁽²⁾_L coincides with the class of Gorenstein (L,A)-projective modules with the help of some special classes of modules.

Firstly,  according to the structural characteristics of Snark graphs, we constructed two classes of 3-regular graphs based on Double Star and Cross. Secondly, we studied the  problem of neighbor full sum distinguishing total coloring of four classes of 3-regular graphs by exhaustive coloring method and combinatorial analysis, and obtained that the neighbor full sum distinguishing total chromatic numbers for these graphs are all 2.

We considered the convergence analysis problem of the inversion of the radiation coefficient of a one-sided degenerate parabolic equation by using known terminal observation data. Firstly, it was necessary to satisfy the Fichera condition for the one-sided degenerate parabolic equation to ensure the solvability of the problem. Secondly, we transformed the original inverse problem into an optimal control problem and found the optimal solution for the radiation coefficient through optimal control methods. Finally, by combining the Gateaux derivative and introducing new source conditions, we proved the convergence of the optimal solution.

By using the fixed point theorem on the cone, the author study a class of  cantilever beam equations{w″″(t)=λf(t,w(t)), t∈(0,1), w(0)=w′(0)=w″(1)=w(1)=0, where λ is a positive parameter, f∈C(［0,1］×［0,∞),［0,∞)). The existence and multiplicity results of its positive solutions are given when the nonlinear term f satisfies superlinear or sublinear growth condition.

Firstly, the concept of quasi-homogeneous kernel was introduced to discuss Hilbert-type integral inequalities with quasi-homogeneous kernel in weighted Lebesgue spaces with exponential functions. Secondly, by using the weight coefficient method and several  analysis techniques, equivalent parameter condition for optimal Hilbert-type integral inequalities was given, and the calculation formula for the best constant factor was obtained. Finally, its applications in operator theory were discussed.

The lifetime problem of a closed discrete renewal censored δ shock model was studied by using condition method and probability method. The explicit expressions of the lifetime properties such as reliability and moment of lifetime of the model were obtained, the lifetime distribution and the mean lifetime of the model were applied to specific distributions and performed numerical simulations.

We  proposed a novel derivative-free algorithm  to solve convex constrained nonlinear equation systems. The  algorithm utilized improved conjugate parameters to design a search direction, ensuring sufficient descent and trust region characteristics of the algorithm. Under appropriate assumptions, the  algorithm had  global convergence. Numerical simulation results show that the  algorithm has high  efficiency and robustness in handling convex constrained nonlinear equation systems and signal reconstruction problems.

The time-adaptive finite element method based on adjacent time steps was used to solve a class of time-dependent Poisson-Nernst-Planck (PNP) equations, which accelerated the efficiency of long-term numerical simulations for solving two-dimensional PNP equations containing multiple ions. Numerical experimental results show  that the method can effectively accelerate computations in both numerical formats and is effective for long-term numerical computation of PNP equations.

By using the method of geometric analysis, we study Ricci-Bourguignon almost solitons with projective vector field. Firstly, if the potential vector field is projective one, we prove that the Ricci-Bourguignon almost solitons have vanishing Cotton tensor field, divergence-free Bach tensor field and Ricci tensor field is conformal Killing tensor field. Secondly,  we prove the K-contact Ricci-Bourguignon almost soliton whose potential vector field is a projective vector field is an Einstein mainfold.

Firstly,  we used the original dual active set method to solve the forward problem of option pricing, with the corresponding numerical solutions as the output for supervised learning, and then replaced the  forward problem model of option pricing with a well-trained neural network. Secondly, we combined Bayesian inference with neural networks for Metropolis-Hastings sampling  to solve the inverse problem of implied volatility. This method reduced the problem of large computational complexity  of the forward problem during the sampling process, thereby accelerating the solution process for the inverse problem.

Based on a domestic mainstream large language model, we designed a question answering system for the Linux course. This system, combined with  retrieval enhancement technology, could continuously learn from human feedback, which helped to solve the problem of how to more effectively assist students’ learning in the Linux course teaching. Experimental results show that the system improves the factuality of answers provided by the large language model and can effectively answer  students’ questions. In addition, the system accumulates a professional domain knowledge base presented in the form of natural language at a  lower cost, reducing the workload of teachers in collecting and organizing teaching materials.

Aiming at the problem of low accuracy and low recommendation efficiency in  the traditional algorithms during the recommendation process of institutional documents, we proposed a text recommendation algorithm based on knowledge embedding. By transforming knowledge in the  knowledge graph  into feature vectors and combining them with neural network models, the accuracy and stability of the recommendation system were effectively improved when dealing with massive and diverse data. Experimental results show that the proposed algorithm exhibits better recommendation accuracy and stability than the traditional methods in the face of cold start and diverse user interests. It provides a more efficient and reliable solution to the data sparsity problem and personalisation requirements in large-scale recommendation systems, which helps to improve the user experience and enhance the overall performance of the recommendation system.

Aiming at  the problems of low search efficiency and susceptibility  to  local optima in  particle swarm optimization algorithm for optimizing  complex engineering problems, we proposed  a house topology-based particle swarm optimization algorithm. By 
 proposing  a house topology and designing a position update strategy tailored to its characteristics, the algorithm improved the information transmission and communication methods of  particle swarm optimization algorithm, thereby enhancing the convergence rate and global optimization capability of the algorithm. The comparative experimental results on benchmark
 functions show that the optimization accuracy, convergence speed, and stability of the house topology-based particle swarm optimization algorithm are superior to the other  4 improved algorithms. The simulation results  on 3 real-world engineering optimization problems further validate the  effectiveness and practicality of the proposed algorithm.

Aiming at the problem that in the field of natural language processing,  incomplete knowledge graphs led to the entity association expansion, which required additional inference and reasoning to make the derivation process of answers  more complex, we proposed  a knowledge graph question answering algorithm  RMP-KGQA that combined relational memory and  path information. The algorithm used a relational memory network to solve  the problem of inconsistency between the problem and the knowledge graph mapping space, and  enriched the scoring function with its path information, significantly enhancing the accuracy and robustness of the intelligent question answering retrieval system. The experimental results show that on the WebQSP and WebQSP-50 benchmark datasets, the accuracy of RMP-KGQA  increases by 2.8 and 2.4 percentage points respectively compared to EmbedKGQA. Ablation experiments further verify  the key roles of relational memory perception and path information in the model. Therefore,  RMP-KGQA is an effective method for solving  multi-hop knowledge graph question answering problems  in complex environments.

Aiming at the problem that  traditional obstacle avoidance search algorithms could only solve single-point distribution and inadequately considered  the needs for multi-point distribution and round-trip pickups in workshop material distribution, we proposed an A* algorithm that combined  a genetic algorithm optimization. This method employed the cost calculation approach of the A* algorithm to complete cost calculation between various distribution points under obstacle conditions, and integrated 
the iterative optimization characteristics of the genetic algorithm to achieve efficient and stable global search for multi-point distribution and round-trip pickup requirements. Through the verification of a practical example of material distribution in a certain workshop, the improved algorithm can effectively plan distribution paths in obstacle environments and  significantly improve distribution efficiency.

Aiming at the problem of optimal harvesting of symbiotic populations in finite time,  we proposed  the optimal harvesting strategy for symbiotic populations by discussing finite-time stability of symbiotic populations, utilizing Pontryagin maximum principle and Hamilton function method. Firstly,  a nonlinear model of the growth process of symbiotic organisms was established based on the data information of the breeding process. Under the condition of ensuring the balance of ecological environment, the finite time stability of the symbiotic growth process and the symbiotic system was deeply analyzed, and a strict proof process was given. Secondly, an optimal harvesting method was derived by applying Pontryagin maximization principle based on Lyapunov method, and the general algorithm of optimal harvesting solution was obtained. Finally,  the effectiveness of  the proposed algorithm was proved by using simulation and comparative experimental results.

Aiming at  the problem of low solution precision in existing optimization algorithms, we proposed a global-local cooperative optimization algorithm with fitness step size.  The algorithm achieved  effective collaboration between global and local search in  the solution space by balancing  individual fitness and dynamically allocating global and local search step sizes during each iteration, thereby enhancing the solution precision. Experimental results show that  the proposed algorithm has  high precision and stability in benchmark function tests, and its effectiveness in solving complex engineering optimization problems is verified through simulation experiments.

Aiming at the problem that the existing associative classifier could not store duplicate samples, we proposed  a design method of associative classifier based on Hamming distance and quantum search algorithm, and gave a line diagram for the storage and classification of the associative classifier. The method required the preparation of  five sets of qubits  in advance to encode Hamming distance, input sample, pattern sample, category and sequence number respectively. Firstly, according to the total N of the sample, the number of qubits required by the associative classifier was calculated, and then the qubits with an  initial state of  |0〉were rotated to an equilibrium superposition state containing exactly N ground states by using the quantum revolving gate and the Hadamard gate. Secondly, according to the category and value of the sample to be stored, the remaining two sets of qubits with initial state of  |0〉 were converted into the corresponding quantum ground state through controllable operation. Finally, based on the classification method of quantum minimum search, the Hamming distance between the input sample and all the stored samples was calculated, and then the fixed phase Grover quantum search algorithm was used to search for the minimum value of these Hamming distances.  The category of the stored sample corresponding to the minimum value was the category of the input sample, and the specific classification results could be obtained by measuring the quantum states in the register.

Aiming at the problem of the need to improve  confidence level in few-shot image classification inference at present, we proposed 
a new model that combined meta-confidence transductive inference, data obfuscation method, and feature-wise linear modulation method. Firstly, by using transductive inference, the model could learn properties of inference data during training process, and achieve targeted learning. Secondly, combining  data obfuscation methods  in the network architecture to enhance the extraction of key features, and  improve the feature discovery ability of the  model.  Finally, feature-wise linear modulation transformation was added to  the transductive inference framework to improve the model’s few-shot query capabilities. The results of experiments conducted on  standard datasets Mini-ImageNet and Tiered-ImageNet show  that the model improves  accuracy by  3.21 and 3.36 percentage points respectively when performing  5-way 1-shot tasks on these two datasets, and by 2.89 and 1.89 percentage points  respectively on 5-way 5-shot tasks. The experimental results validate the effectiveness of the proposed method.

Aiming at the problems that it was difficult to accurately identify the key information of fine-grained images, the classification index was relatively simple and the feature utilization was not sufficient in existing models, we  proposed a new  fine-grained image classification network model. In the network training step, the model embedded a dual attention network to strengthen the correlation between middle-level features and depth features. According to the different receptive field sizes of different layers of the network, the data were trimmed and then spliced into new sample data as the input for the next layer. The support vector machine classifier was used to take the output results of middle-level features and depth features together as the final classification index.  The experimental results  on three classic datasets CUB-200-2011, Stanford Cars and 102 Category Flower show that the classification accuracy reaches 89.56%, 95.00% and 96.05%, respectively. Compared with other network models, it has better classification accuracy and generalization ability.

Through the propagation of electromagnetic waves in the medium and the continuous conditions of the tangential components of electric and magnetic fields at the interface between the medium and the medium, we gave the transmission matrix of light propagation in the medium and the matching matrix of light at the interface of the medium, respectively, so as to obtain the total transmission matrix of the combined structure photonic crystal and their reflectance. On this basis, we studied the inverted symmetric combined structures for (ABA)^N(BAB)^M photonic crystal interface states. By changing the refractive index coefficient n_a0, parameter e, thickness d_a and period number N of the medium A, as well as the mass concentration of medium B (glucose solution), temperature, the thickness of d_b and period number M, and the size of the incident angle, we gave the location of the interface state and the peak size curve along with the change of these parameters, and studied the effects of the mass concentration of glucose solution on multiple interface states of combined structures PC₁+PC₂+PC₁ and PC₁+PC₂+PC₁+PC₂+PC₁. The numerical calculation results show that the location of the interface state and peak size can be changed when the mass concentration of glucose is changed, thereby achieving the adjustment of the interface state.

Polyimide had the characteristics such as resistance to high temperatures, flexibility, easy adhesion, good mechanical extensibility and tensile strength, we prepared infrared thermal insulation and protective films on a flexible polyimide material with a thickness of 125 μm. During the preparation process, the adhesion of the film layer on the flexible substrate could be improved by adjusting the energy of the ion source. Based on the principle of least squares, a relationship formula was established between the optical constants of the film material and temperature to solve the influence of temperature changes on the optical performance of the thin film. In the deposition of diamond-like carbon (DLC) film, the preheating method was used to solve the problem of uneven film thickness caused by the deformation of the flexible substrate. The infrared spectroscopy detection and analysis show that the infrared thermal insulation film prepared on the polyimide substrate meets the usage requirements.

Aiming at the problem of microwave heating uniformity, we designed a new curved slot waveguide heating structure based on the theory of slot array antenna. The results show that the design improves the electric field uniformity inside the heating cavity through random superposition of the electric fields radiated by multiple slots. The curved surface structure design makes it easier to conformally align with the cylindrical heating cavity, while reducing the volume of the entire microwave heater. After heating the rubber with a thickness of 5 mm for 20 s, the temperature difference coefficient （COV） reaches 0.56, which is 60% higher than the traditional box type microwave heating device with the same power density, and the uniformity is better improved.

The enantiomerism transformation mechanism of bivalent magnesium valine complexes (Val·Mg²⁺) in physiological environment was studied by using M06-2X and MN15 hybrid exchange functional methods for dealing with remote weak interactions of density functional theory and SMD model method (for solvent effects). The results of the study on enantiomerism reaction channels show that there are three enantiomerism reaction channels of chiral Val·Mg²⁺, which are H proton uses carbonyl O as a bridge,  carbonyl O combined with amino N as a bridge,  and amino N as a bridge alone. The calculation of free energy potential energy surface of the reaction process shows that it is advantageous for H proton using amino N as a bridge alone for migration reaction. Under the polarity of the water solvent, the energy barrier for speed control step of the dominant reaction channel is 210.4 kJ/mol,  and the catalysis of water molecules (clusters) reduces the energy barrier to 116.1—118.3 kJ/mol. The  enantiomization rate of bivalent magnesium valine complexes in the aqueous liquid phase is extremely slow,  and it can be  safely  used to complement bivalent magnesium ions and valine in living organisms.

The binding characteristics and stability of coreopsin with CYP3A4/CYP2D6 was studied by  using spectroscopy analysis and computer simulation techniques. The results show that the intrinsic fluorescence of cytochrome P450 proteins (CYPs) is quenched mainly by static quenching and supplemented by dynamic quenching. The binding capacity of coreopsin with CYP3A4 is greater than that of CYP2D6. The coreopsin interacts with  CYPs to form a complex. The binding of coreopsin to CYPs leads to changes in  the secondary structure of CYPs. The coreopsin mainly binds to CYPs through hydrogen bonds and van der Waals forces. The  complex formed by coreopsin and two types of CYPs is stable.

Aiming at the shortcomings of traditional adsorption materials, such as low adsorption capacity,  difficulty in solid-liquid separation,  and easy to lead to secondary pollution,  carboxymethyl cellulose (CMC),  polyvinyl alcohol (PVA),  acrylic acid (AA),  and zinc ferrite (ZnFe₂O₄) were used as monomers to prepare CMC/PVA/PAA/ZnFe₂O₄ cellulose based magnetic hydrogels that was easy to form,  low toxicity,  large adsorption capacity,  and could be separated by magnetic remote control through aqueous solution polymerization. Their morphological structure and structural performance were characterized by scanning electron microscopy (SEM),  Fourier transform infrared spectroscopy (FT-IR),  X-ray diffraction (XRD),  and vibrating sample magnetometer (VSM). The adsorption kinetics and thermodynamics were used to investigate their adsorption performance on levofloxacin (LEV) in water and adsorption mechanism. The results show that loaded ZnFe₂O₄  magnetic nanoparticles can increase the magnetic remote separation ability and adsorption ability of hydrogels.   The maximum adsorption capacity of the hydrogel for LEV can reach 405 mg/g at 25 ℃,  pH=5 and 4 h of adsorption,  and its adsorption capacity can still reach 84% of the original adsorption capacity after five adsorption and desorption experiments.  The adsorption process of hydrogel for LEV is more in line with the quasi second order reaction kinetics and intraparticle diffusion model,  and follows the Freundlich isotherm model.